Abstract
Planet formation is generally described in terms of a system containing the host star and a protoplanetary disk1,2,3, of which the internal properties (for example, mass and metallicity) determine the properties of the resulting planetary system4. However, (proto)planetary systems are predicted5,6 and observed7,8 to be affected by the spatially clustered stellar formation environment, through either dynamical star–star interactions or external photoevaporation by nearby massive stars9. It is challenging to quantify how the architecture of planetary sysems is affected by these environmental processes, because stellar groups spatially disperse within less than a billion years10, well below the ages of most known exoplanets. Here we identify old, co-moving stellar groups around exoplanet host stars in the astrometric data from the Gaia satellite11,12 and demonstrate that the architecture of planetary systems exhibits a strong dependence on local stellar clustering in position-velocity phase space. After controlling for host stellar age, mass, metallicity and distance from the star, we obtain highly significant differences (with p values of 10−5 to 10−2) in planetary system properties between phase space overdensities (composed of a greater number of co-moving stars than unstructured space) and the field. The median semi-major axis and orbital period of planets in phase space overdensities are 0.087 astronomical units and 9.6 days, respectively, compared to 0.81 astronomical units and 154 days, respectively, for planets around field stars. ‘Hot Jupiters’ (massive, short-period exoplanets) predominantly exist in stellar phase space overdensities, strongly suggesting that their extreme orbits originate from environmental perturbations rather than internal migration13,14 or planet–planet scattering15,16. Our findings reveal that stellar clustering is a key factor setting the architectures of planetary systems.
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Data availability
The Gaia data used in this work are publicly available through the Gaia archive (https://gea.esac.esa.int/archive/). The exoplanetary catalogue used in this work is publicly available through the NASA Exoplanet Archive (https://exoplanetarchive.ipac.caltech.edu/). Results of the calculations performed as part of this work are either available in the Supplementary Information, or from the authors upon request. A table containing the planet properties, host star properties, and the phase space decomposition is publicly available at https://github.com/ajw278/astrophasesplit with file name planetdata (2).csv.
Code availability
The code used for the phase space decomposition is publicly available at https://github.com/ajw278/astrophasesplit.
Change history
19 January 2021
A Correction to this paper has been published: https://doi.org/10.1038/s41586-020-03096-5
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Acknowledgements
A.J.W. thanks R. Alexander for discussions. A.J.W. acknowledges funding from the Alexander von Humboldt Stiftung in the form of a Postdoctoral Research Fellowship and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 681601). J.M.D.K. and M.C. acknowledge funding from the German Research Foundation (DFG) in the form of an Emmy Noether Research Group (grant no. KR4801/1-1) and the DFG Sachbeihilfe (grant no. KR4801/2-1). J.M.D.K. acknowledges funding from the ERC under the European Union’s Horizon 2020 research and innovation programme via the ERC Starting Grant MUSTANG (grant agreement no. 714907). This research made use of data from the European Space Agency mission Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, http://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.
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A.J.W. led the study, developed the analysis method, and performed the analysis, with contributions from J.M.D.K. and S.N.L. A.J.W. and J.M.D.K. wrote the text, with contributions from S.N.L. and M.C. J.M.D.K. and M.C. developed the initial idea for the project. All authors contributed to aspects of the analysis and the interpretation of the results.
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Extended data figures and tables
Extended Data Fig. 1 Probability density functions of the relative phase space density for synthetic stellar populations.
Blue histograms represent the distribution of \({\tilde{\rho }}_{{\rm{M}},20}\) for a background (‘field’) population, while red histograms represent a population of stars with a spatial density perturbed by a multiplicative factor δρ* (increasing from left to right, a, d, g–c, f, i) and with a velocity dispersion perturbed by a multiplicative factor δσv (increasing from top to bottom; a, b, c–g, h, i). Outlined purple histograms show the sum of the perturbed and background populations. The solid black line represents a double-lognormal fit to this combined phase space density distribution, with both lognormal components marked by dotted lines. The multiplicative factors by which the density and velocity dispersion are perturbed (numbers in brackets are the values of δρ* and δσv inferred from the phase space density decomposition), as well as the probability that the distribution can be described by a single lognormal (Pnull) are shown.
Extended Data Fig. 2 Effect of the choice of threshold probability on the median exoplanet properties in environments with low and high phase space density.
The panels show the median orbital period (a), orbital eccentricity (b), and planet mass (c), for the same exoplanet host star sample as in Fig. 3. Exoplanets orbiting field stars (Plow > Pth) are shown in blue, and exoplanets orbiting stars within overdensities (Phigh > Pth) are shown in red. The median of the full sample is shown as a dashed black line, and the chosen Pth = 0.84 (adopted for our main results) is shown as a vertical black line.
Extended Data Fig. 3 Normalized cumulative distribution functions of planet and host star properties.
The samples are divided into low (blue) and high (red) host star phase space densities, without applying any cuts in host star age or mass (unlike in Fig. 3). The panels are the same as in Fig. 3 (a–f for exoplanet properties, g–j for stellar host properties). The faint lines represent 100 Monte Carlo control experiments, constructed by drawing a star at random from within 40 pc of each exoplanet host and using the phase space density of that star instead. The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test for the exoplanet hosts (black) and for the median of all control experiments (grey; including 16th–84th percentile uncertainties) are shown.
Extended Data Fig. 4 Normalized cumulative distribution functions of exoplanet properties that exhibit bimodal distributions.
The samples are divided into low (blue) and high (red) host star phase space densities. The sample is split across the top and bottom rows by semi-major axes (a, <0.3 au; d, >0.3 au), planet masses (b, <50M⊕; e, >50M⊕), and radii (c, <5R⊕; f, >5R⊕). The distributions are shown for the same exoplanet host sample as in Fig. 3. The faint lines represent 100 Monte Carlo control experiments, constructed by drawing a star at random from within 40 pc of each exoplanet host and using the phase space density of that star instead. The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test for the exoplanet hosts (black) and for the median of all control experiments (grey; including 16th–84th percentile uncertainties) are shown.
Extended Data Fig. 5 Normalized cumulative distribution functions of planet and host star properties in our fiducial sample, limiting the sample to systems within 300 pc of the Sun (unlike in Fig. 3).
The samples are divided into low (blue) and high (red) host star phase space densities. The panels are the same as in Fig. 3 (a–f for exoplanet properties, g–j for stellar host properties). The faint lines represent 100 Monte Carlo control experiments, constructed by drawing a star at random from within 40 pc of each exoplanet host and using the phase space density of that star instead. The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test for the exoplanet hosts (black) and for the median of all control experiments (grey; including 16th–84th percentile uncertainties) are shown.
Extended Data Fig. 6 Normalized cumulative distribution functions of the kinematic properties of the host stars.
Panel a shows the distribution of absolute proper motions, whereas panel b shows the same for radial velocities. The distributions are shown for all exoplanet host stars that have age and mass estimates. The sample is split by exoplanet discovery method (radial velocity in green, transit in orange) and both subsamples have the same distance distribution by construction (see Methods). The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test between the two survey types are shown.
Extended Data Fig. 7 Normalized cumulative distribution functions of host star properties in the complete sample of Extended Data Fig. 3.
The sample is divided into exoplanets discovered by radial velocity (a–c) and transit (d–f) surveys. Red lines indicate exoplanet host stars that occupy a phase space overdensity, whereas blue lines represent host stars in the field. For reference, the distributions of the entire host star sample (including all detection methods) from Extended Data Fig. 3 are shown as dashed lines. The logarithms of p values obtained from a two-tailed Kolmogorov–Smirnov test are shown.
Extended Data Fig. 8 Distributions of exoplanet semi-major axes and masses split by ambient stellar phase space density for different planet discovery methods.
Columns indicate low (a, c; Plow > 0.84) and high (b, d; Phigh > 0.84) phase space densities (as in Fig. 2), split into rows of exoplanets discovered by transit (a, b) and radial velocity (c, d) surveys. Data points with grey error bars (indicating 1σ uncertainties) show individual planets and contours show a two-dimensional Gaussian kernel density estimate. The dashed black lines in a and c follow \({M}_{{\rm{p}}}\propto {a}_{{\rm{p}}}^{1.5}\) and illustrate the 1σ scatter around an orthogonal distance regression to all planets orbiting field stars that are not hot Jupiters (see Fig. 2a). For reference, b and d includes the Solar System (Phigh = 0.89) planets within ap < 10 au.
Extended Data Fig. 9 Phase space distributions of stars near the three exoplanet host stars HD 104067, HAT-P-3 and HD 285968.
Panels a–c show the phase space density distributions (purple histograms), together with the best-fitting double-lognormal function (black solid line) and the individual lognormal components (black dashed lines) obtained by Gaussian mixture modelling. Keys list the probability that the density distribution is described by a single lognormal (red line) as Pnull, and the probability that each exoplanet host is associated with a phase space overdensity as Phigh. Panels d–f show the azimuthal (vϕ) and radial (vr) components of the stellar velocities in galactocentric coordinates. Stars in overdensities are shown in red, whereas field stars are shown in blue. To divide the stars into a low- and high-density population, we apply a Monte Carlo procedure that randomly assigns stars based on their individual probabilities of belonging to either of the two components (equation (5)). The host star velocity is shown as a star symbol. These three host stars illustrate cases of a highly significant (Phigh = 0.05) low phase space density (HD 104067), a highly significant (Phigh = 0.94) phase space overdensity (HAT-P-3) and an ambiguous (Phigh = 0.45) phase space density (HD 285968).
Extended Data Fig. 10 Age distributions of exoplanet host stars with masses 0.7M☉−2M☉.
The red histogram shows stars in overdensities (Phigh > 0.84) and the blue histogram shows field stars (Plow > 0.84). The faint lines represent the results of performing 200 Monte Carlo realizations of the ages, drawn from normal distributions defined by the measured ages and their uncertainties. The error bars show the 16th–84th percentile range of the resulting age distributions.
Supplementary information
Supplementary Table 1
The results of all the calculations we performed for each exoplanet host star in the NASA Exoplanet Archive with available six-dimensional astrometry in Gaia DR2.
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Winter, A.J., Kruijssen, J.M.D., Longmore, S.N. et al. Stellar clustering shapes the architecture of planetary systems. Nature 586, 528–532 (2020). https://doi.org/10.1038/s41586-020-2800-0
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DOI: https://doi.org/10.1038/s41586-020-2800-0
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